Cluster expansion made easy with Bayesian compressive sensing

Abstract

Long-standing challenges in cluster expansion (CE) construction include choosing how to truncate the expansion and which crystal structures to use for training. Compressive sensing (CS), which is emerging as a powerful tool for model construction in physics, provides a mathematically rigorous framework for addressing these challenges. A recently-developed Bayesian implementation of CS (BCS) provides a parameterless framework, a vast speed up over current CE construction techniques, and error estimates on model coefficients. Here, we demonstrate the use of BCS to build cluster expansion models for several binary alloy systems. The speed of the method and the accuracy of the resulting fits are shown to be far superior than state-of-the-art evolutionary methods for all alloy systems shown. When combined with high throughput first-principles frameworks, the implications of BCS are that hundreds of lattice models can be automatically constructed, paving the way to high throughput thermodynamic modeling of alloys

Efficient determination of alloy ground-state structures

“…A combination of DFT calculation and the cluster expansion (CE) method [14][15][16] is also useful for alloys. Recent progress in combining the CE method with DFT calculations [17][18][19][20][21][22][23][24][25][26][27][28] has enabled us to evaluate the ground-state structures and phase stability accurately. Although it is impossible to find structures beyond a given crystal lattice using the ordinary CE method, many yet-unobserved structures have been discovered within alloy configurations on the crystal lattice.…”

Lattice Anharmonicity and Thermal Conductivity from Compressive Sensing of First-Principles Calculations

“…We have recently shown that a similar problem in alloy theory, the cluster expansion (CE) method for configurational energetics [21,22], can be solved efficiently and accurately using compressive sensing [23,24]. CS has revolutionized information science by providing a mathematically rigorous recipe for reconstructing S-sparse models (i.e., models with S nonzero coefficients out of a large pool of possibles, N , when S N ) from a set of only O(S) data points [25][26][27].…”

“…(4). For the discrete orthogonal basis in the CS cluster expansion [23,24], i.i.d. sensing matrices A could be obtained by enumerating all ordered structures up to a certain size and choosing those with correlations that map most closely onto quasi-random vectors.…”

Multiscale ab initio simulation of Ni-based alloys: Real-space distribution of atoms in γ + γ ′ phase

“…The ''best'' model for the alloy system is obtained by minimizing the cross-validation score S CV , in the spirit of model-selection approaches. Several innovative algorithms have been developed for this purpose [14][15][16][17][18][19]22,23] techniques. Among these, the GA-based algorithm, which performs unbiased search, is noteworthy since the resultant cluster set a does not obey the hierarchical and compactness conditions.…”

“…In earlier implementation of DFT + CEMC, the set {a} were intuitively selected or progressively expanded to improve predictability. In recent years, methods from the field of regression analysis, machine learning and signal processing, which includes genetic algorithm (GA) [14], variational method [15], Bayessian approach [16,17], and compressive sensing algorithm [18,19], have been applied to the problem of finding {a} leading to highly accurate cluster expansion (CE). These algorithms are based on general strategy to minimize the cross-validation score S CV which represent the error between CE predicted energy and DFT energy not used in the training set.…”